A STEADY-STATE SYSTEM IN NONEQUILIBRIUM THERMODYNAMICS INCLUDING THERMAL AND ELECTRICAL EFFECTS

The steady-state equations for a charged gas or fluid consisting of se veral components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equa tions which in some situations can be derived from the Boltzmann equat ion. The model uses the duality between the thermodynamic fluxes and t he thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions are prescribed. The existence of generalized solut ions is proven. The key of the proof is a transformation of the proble m by using the entropic variables, or electro-chemical potentials, whi ch symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the ther mal equilibrium. A general uniqueness result cannot be expected for ph ysical reasons. (C) 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Lt d.